What type of trapezoid must have a pair of parellel sides and a pair of congruent sides?

At what interest rate (to the nearest hundredth of a percent) compounded annually will money in savings double in five years?

Sphinxa [80]

For a single payment with compound interest, the equation to use is F=P(1+i)^n where F is the value after n periods, P is the present value, and i is the interest rate.

If we want the final value F to double in 5 years, F is then equal to P then n=5. The equation is now:

2P=P(1+i)^5
2=(1+i)^5
i=14.87% per year

5 0

3 years ago

Molly earns a rebate each month on her movie tickets and books. She earns $0.25 for each movie ticket and $2 for each book. Last

UNO [17]

the algebraic expression is 4(0.25)+2x=17

STEP 1: Simplify both sides of the equation

1+2x=17 or 2x+1=17

STEP 2: Subtract 1 from both sides

2x=16

STEP 3: Divide both sides by 2

2x/2 = 16/2

x=8

6 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP 30 PTS ):

ASHA 777 [7]

Answer:

Step-by-step explanation:

It's an exponential function but it is going in the negative direction. So now you know there has to be a negative in front of the function meaning it can only be c or d. Since we know its a exponential function. If we set x = 0, it will give us the y intercept. Which should be 1. However it is -2. Therefore it it multiplied by -2 meaning d is right answer

6 0

3 years ago

Read 2 more answers

You are planning a survey of starting salaries for recent computer science majors. In a recent survey by the National Associatio

nydimaria [60]

Answer:

A sample size of 554 is needed.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Standard deviation is known to be $12,000

This means that $\sigma = 12000$

What sample size do you need to have a margin of error equal to $1000, with 95% confidence?

This is n for which M = 1000. So

$M = z\frac{\sigma}{\sqrt{n}}$

$1000 = 1.96\frac{12000}{\sqrt{n}}$

$1000\sqrt{n} = 1.96*12$

Dividing both sides by 1000:

$\sqrt{n} = 1.96*12$

$(\sqrt{n})^2 = (1.96*12)^2$

$n = 553.2$

Rounding up:

A sample size of 554 is needed.

5 0

3 years ago

These data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. Accordi

CaHeK987 [17]

Answer:

First part

$P(X< 3.4-0.6*3.1) = P(X$

And for this case we can use the z score formula given by:

$z = \frac{x- \mu}{\sigma}$

And using this formula we got:

$P(X$

And we can use the normal standard table or excel and we got:

$P(Z$

Second part

For the other part of the question we want to find the following probability:

$P(-1.715$

And using the score we got:

$P(-1.715$

And we can find this probability with this difference:

$P(-1.65< Z< 1.210)=P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the data of a population, and for this case we know the distribution for X is given by:

$X \sim N(3.4,3.1)$

Where $\mu=3.4$ and $\sigma=3.1$

First part

And for this case we want this probability:

$P(X< 3.4-0.6*3.1) = P(X$

And for this case we can use the z score formula given by:

$z = \frac{x- \mu}{\sigma}$

And using this formula we got:

$P(X$

And we can use the normal standard table or excel and we got:

$P(Z$

Second part

For the other part of the question we want to find the following probability:

$P(-1.715$

And using the score we got:

$P(-1.715$

And we can find this probability with this difference:

$P(-1.65< Z< 1.210)=P(Z$

8 0

3 years ago